In: Finance
Today’s price of Delta Airlines (DAL) is $30 per share. DAL does not pay dividends. The annualized volatility of DAL is 45 percent. The c.c. risk-free interest rate is ten percent. Assume there is no arbitrage and the Black-Scholes model assumptions hold.
What is the price of a European put option on DAL with a strike of $40 and a maturity of one year?
Solution>
The price of the European put option is $9.48
I have solved it in Excel. The formula used are written in the column along with the values. If you still have any doubt, kindly ask in the comment section.
Type of Option | Put Option | |
Stock Price (S0) | $ 30.00 | |
Exercise (Strike) Price (K) | $ 40.00 | |
Time to Maturity (in years) (t) | 1.00 | |
Annual Risk Free Rate (r) | 10.00% | |
Annualized Volatility (σ) | 45.00% | |
Option Price | $ 9.48 | =K*e-rt*N(-D2)-S0*N(-D1) |
Additional Calculation Parameters | ||
ln(S0/K) | (0.288) | |
(r+σ2/2)t | 0.201 | |
σ√t | 0.450 | |
d1 | (0.192) | =(ln(S0/K)+(r+σ2/2)t)/σ√t |
d2 | (0.642) | =D1-σ√t |
N(d1) | 0.424 | =NORM.S.DIST(d1) |
N(d2) | 0.260 | =NORM.S.DIST(d2) |
N(-d1) | 0.576 | =NORM.S.DIST(-d1) |
N(-d2) | 0.740 | =NORM.S.DIST(-d2) |
e-rt | 0.90484 |
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